POST UTME IGBINEDION UNIVERSITY 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \( 2^x > 10 \) u\sing \logarithms.
A. \( x > 3.3219 \)
B. \( x < 3.3219 \)
C. \( x > 1.5 \)
D. \( x < 1.5 \)
Question 2
Solve the quadratic equation \( x^2 + 4x - 5 = 0 \).
A. \( x = -5, x = 1 \)
B. \( x = -1, x = 5 \)
C. \( x = -2, x = 2.5 \)
D. \( x = -1, x = 5 \)
Question 3
Solve the equation \( x^2 + 4x + 4 = 0 \).
A. \( x = -2 \)
B. \( x = 2 \)
C. \( x = -1 \)
D. \( x = 1 \)
Question 4
Find the probability of drawing two hearts from a s\tandard deck of 52 cards.
A. \( \frac{1}{221} \)
B. \( \frac{1}{52} \)
C. \( \frac{1}{26} \)
D. \( \frac{1}{13} \)
Question 5
Find the sum of the first 10 terms of the arithmetic sequence ( 2, 5, 8, ldots ).
A. 50
B. 55
C. 60
D. 65
Question 6
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).
A. 16
B. 20
C. 24
D. 28
Question 7
Find the equation of the \tangent to the curve \( y = \frac{1}{2}x^2 - 3x + 2 \) at the point where \( x = 1 \).
A. \( y = x - 5 \)
B. \( y = -2x + 3 \)
C. \( y = 2x - 1 \)
D. \( y = x + 1 \)
Question 8
Let X and Y be indep\endent random variables with probability density functions f_X(x) = 2x, 0 < x < 1, and f_Y(y) = 3y^2, 0 < y < 1. Find the probability that X + Y < 1.
A. 1/4
B. 1/2
C. 3/4
D. 1
Question 9
If u = \sin^3 x, find \frac{du}{dx} u\sing the chain rule.
A. 3\sin^2 x \cos x
B. \cos x
C. \sin x
D. \cos^3 x
Question 10
Find the determinant of the matrix \[ \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix} \]
A. 0
B. 1
C. 2
D. 3
Question 11
Find the vector \( mathbf{a} + mathbf{b} \) if \( mathbf{a} = 2mathbf{i} + 3mathbf{j} \) and \( mathbf{b} = mathbf{i} - 2mathbf{j} \).
A. \( 3mathbf{i} + mathbf{j} \)
B. \( 3mathbf{i} - mathbf{j} \)
C. \( mathbf{i} + 5mathbf{j} \)
D. \( 3mathbf{i} + 5mathbf{j} \)
Question 12
Solve the system of equations u\sing matrices: \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 3 \\ 8 \end{bmatrix}
A. x = 1, y = 2
B. x = 2, y = 1
C. x = 3, y = 4
D. x = 4, y = 3
Question 13
Find the equation of the circle with centre ( (2, 3) ) and radius ( 4 ).
A. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
B. \( x + 2 \ \)^2 + \( y - 3 \)^2 = 16 )
C. \( x - 2 \ \)^2 + \( y + 3 \)^2 = 16 )
D. \( x + 2 \ \)^2 + \( y + 3 \)^2 = 16 )
Question 14
Find the equation of the circle with center at (2, 3) and pas\sing through the point (4, 5).
A. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 9 )
B. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 25 )
D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 36 )
Question 15
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)
B. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 + \frac{1}{2} \)
C. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 - \frac{1}{2} \)
D. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)

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